FIG. 1 is a schematic axial view of a conventional third generation CT scanner 10 which includes an x-ray source 12 and an x-ray detector system 14 secured to diametrically opposite sides of an annular shaped disk 16. The disk 16 is rotatably mounted within a gantry support (not shown), so that during a scan the disk 16 continuously rotates about a longitudinal z-axis while x-rays pass from the source 12 through an object, such as a patient 20, positioned on a patient table 56 within the opening of the disk 16. The z-axis is normal to the plane of the page in FIG. 1 and intersects the scanning plane at the mechanical center of rotation 18 of the disk 16. The mechanical center of rotation 18 of the disk corresponds to the "isocenter" of the reconstructed image.
In one conventional system, the detector system 14 includes an array of individual detectors 22 disposed in a single row in a shape of an are having a center of curvature at the point 24, referred to as the "focal spot," where the radiation emanates from the x-ray source 12. The source 12 and array of detectors 22 are positioned so that the x-ray paths between the source and each detector all lie in a "scanning plane" that is normal to the z-axis. Since the x-ray paths originate from what is substantially a point source and extend at different angles to the detectors, the diverging x-ray paths form a "fan beam" 26 that is incident on the detector array 14 in the form of one-dimensional linear projection. The x-rays incident on a single detector at a measuring instant during scan are commonly referred to as a "ray," and each detector generates an output signal indicative of the intensity of its corresponding ray. The angle of a ray in space depends on the rotation angle of the disk and the location of the detector in the detector array. Since each ray is partially attenuated by all the mass in its path, the output signal generated by each detector is representative of the attenuation of all the mass disposed between that detector and the x-ray source, i.e., the attenuation of the mass lying in the detector's corresponding ray path. The x-ray intensity measured by each detector is converted by a logarithm function to represent a line integral of the object's density, i.e., the projection value of the object along the x-ray path.
The output signals generated by the x-ray detectors are normally processed by a signal processing portion (not shown) of the CT system. The signal processing portion generally includes a data acquisition system (DAS) which filters the output signals generated by the x-ray detectors to improve their signal-to-noise ratio (SNR). The output signals generated by the DAS during a measuring interval are commonly referred to as a "projection", "projection profile", or "view" and the angular orientation of the disk 16, source 12 and detector system 14 corresponding to a particular projection profile is referred to as the "projection angle."
If the detector array consists of N detectors, then N projection values are collected for each rotation angle. With the rays in a fan shape, these N projection values are collectively called a fan-beam projection profile of the object. The data of fan-beam projection profiles are often reordered or rebinned to become parallel-beam projection profiles. All rays in a parallel-beam profile have the same angle, called the parallel-beam projection view angle .phi.. The image of the object can be reconstructed from parallel-beam projection profiles over a view angle range of 180.degree..
During a scan, the disk 16 rotates smoothly and continuously around the object being scanned, allowing the scanner 10 to generate a set of projections at a corresponding set of projection angles. In a conventional scan, the patient remains at the constant z-axis position during the scan. When obtaining multiple scans, the patient is stepped along the longitudinal z-axis between scans. These processes are commonly referred to as "step-and-shoot" scanning or "constant-z-axis" (CZA) scanning. Using well-known algorithms, such as the inverse Radon transform, a tomogram may be generated from a set of projections that all share the same scanning plane normal to the z-axis. This common scanning plane is typically referred to as the "slice plane."
A tomogram is a representation of the density of a two-dimensional slice along the slice plane of the object being scanned. The process of generating a tomogram from the projections is commonly referred to as "reconstruction," since the tomogram may be thought of as being reconstructed from the projection data. The reconstruction process can include several steps including reordering to form parallel-beam data from the fan-beam data, convolution to deblur the data, and back projection in which image data for each image pixel is generated from the projection data. In CZA scanning, for a particular image slice, all the projections share a common scanning plane, so these projections may be applied directly for convolution and to the back projector for generation of a tomogram.
The step-and-shoot CZA scanning approach can be a slow process. During this time consuming approach, the patient can be exposed to high amounts of x-ray radiation. Also, as the scanning table is moved between each scan, patient motion can result, causing motion and misregistration artifacts which result in reduced image quality.
Several approaches have been developed to decrease the time required to obtain a full scan of an object. One of these approaches is helical or spiral scanning in which the object being scanned is translated along the z-axis while the disk 16 with source 12 and linear detector array 14 are rotated about the patient. In helical scanning, the projections are normally acquired such that the position z is linearly related to the view angle. This form of helical scanning is commonly referred to as constant-speed-helical (CSH) scanning.
FIG. 2A illustrates the data collected during a conventional CZA scan, and FIG. 2B illustrates the data collected during a CSH scan. As shown in FIG. 2A, if the x-ray source 12 and the detector system 14 are rotated about the object 20 while the object remains at a fixed z-axis location, the scanning planes associated with all the projections collected by the detector system 14 will all lie in a common slice plane 50. As shown in FIG. 2B, if the object 20 is continuously translated in the direction of the z-axis while the disk is rotated about the object 20, none of the scanning planes will be coplanar. Rather, the scanning plane associated with each projection will lie at a unique position along the z-axis at a locus point on a helical set of loci. FIG. 2B illustrates the z-axis coordinate of the scanning planes corresponding to helical projection angles in the interval (0, 10.pi.).
In CZA scanning, all the projections share a common scanning plane, so these projections may be applied to the back projector after convolution to generate a tomogram. In CSH scanning however, each projection has a unique scanning plane located at a unique z-axis coordinate, so CSH projections may not be applied to a back projector. However, the data collected during a CSH scan can be interpolated in various fashions to generate a set of interpolated projections that do all share a common scanning plane extending normal to the z-axis. Each interpolated projection, for example, may be generated by combining two projections taken at equivalent projection angles and at different z-axis positions. These interpolated projections may be treated as CZA data and applied after convolution to a back projector to generate a tomogram.
CSH scanning requires some form of interpolation to generate a tomogram, and tomograms generated by CSH scanning therefore tend to be characterized by image artifacts. Also, since the CSH scan projection data, which are collected over an interval of z-axis locations, are combined to generate the interpolated CZA scan data, tomograms generated during CSH scanning have a wider effective slice plane width and, therefore, lower z-axis resolution, than tomograms generated by CZA scanning. However, helical scanning advantageously permits rapid scanning of a large volume of a patient. For example, in a time interval short enough to permit a patient comfortably to hold his or her breath (and thereby remain relatively motionless), a helical scan can collect enough data to fully scan an entire organ such as a kidney.
Another approach to decreasing scan time over CZA scanning is commonly referred to as "cone-beam scanning," in which a three-dimensional volume of the object or patient is scanned at once. In cone-beam scanning, the detection system includes a two-dimensional array of detectors instead of the one-dimensional array used in conventional scanning. The x-ray output from the source diverges in two dimensions to produce the equivalent of multiple fan beams, referred to as a "cone beam," along the z-axis dimension which illuminate multiple rows of plural detectors and therefore form a two-dimensional projection on the array.
In one form of a cone-beam system, the patient or object is maintained in a stationary z-axis position while the source and two-dimensional detector array are rotated around the patient or object. The patient is then moved to a new z-axis position, and the scan is repeated. In this type of step-and-shoot or "stationary cone beam" system, rather than sweeping out a plane, a volume of the object is scanned. After one volume is scanned, the source and detector are stepped along the z-axis to scan the next volume. Still another approach used to decrease scan time is helical cone-beam (HCB) scanning, in which a cone-beam configuration, i.e., a source and two-dimensional detector array, are rotated around the patient while the patient is continuously translated in the z-direction.
One approach to reconstructing volumetric image data is to divide it into a stack of slices. Standard two-dimensional reconstruction techniques, such as 2D filtered back projection (FBP), are used to reconstruct CZA and interpolated CSH data in non-cone-beam systems. FBP requires that the set of projections used for reconstruction of slices lie in the same plane. This condition is satisfied in CZA scanning, and interpolation is used in CSH scanning to produce a set of interpolated or simulated linear projections which effectively meet this requirement. In either case, 2D FBP is an efficient means of producing image data from the 1D fan beam projection data.
In cone-beam geometry, the required condition is only satisfied for a detector row coplanar with the source in a plane perpendicular to the z-axis, usually the center detector row. An image data slice perpendicular to the z-axis will be referred to herein as a normal slice. Other slices, i.e., slices which form a non-perpendicular angle with the z-axis, are referred to herein as oblique slices or tilted slices. In cone-beam CT, a 1D projection defined by the source and a given detector row will intersect a different slice in the object as the gantry rotates. For a helical cone beam scan, no slice is coplanar with the rays in all view angles. Conventional 2D FBP can be used to reconstruct cone-beam data by treating each row as an independent 1D projection. This approximation ignores the cone-beam geometry and results in image artifacts such as streaks and lowering of the reconstructed density.
The approximation can be improved by selecting certain oblique slices for the 2D reconstruction. One such approach is described in U.S. Pat. No. 5,802,134 (the '134 patent), entitled "Nutating Slice CT Image Reconstruction Apparatus and Method," and assigned to the same assignee as the present application. The contents of that patent are incorporated herein in their entirety by reference. In the approach described in the '134 patent, a 2D fan-beam projection profile can be interpolated from the cone-beam data for each slice at each rotation angle. The slice can be reconstructed from the fan-beam projection profiles over a sufficient number of rotation angles. In this prior method, the projection profiles are interpolated directly from the actual cone-beam data. The mathematical relation between the interpolated rays of a projection profile and the original rays are complex. Because of this complexity, the prior method included a procedure based on computer simulation of scanning the oblique slice to determine the locations of interpolating rays. The result of the simulation depends on the accuracy of simulation.
An approximate method used to reconstruct stationary cone-beam data is known as the Feldkamp algorithm and is described in L. A. Feldkamp, et al.,"Practical cone-beam algorithm," J. Opt. Soc. Am. 1, pp. 612-619, (1984).
In the Feldkamp algorithm, the rays are back projected in the three-dimensional cone. Algorithms such as Feldkamp, which attempt to incorporate the true cone-beam geometry of the data, are referred to as three-dimensional filtered back projection (3D-FBP) algorithms. Three-dimensional algorithms reconstructing HCB data have also been developed. Examples of these algorithms are described in the following papers.
1. H. Kudo and T. Saito, "Three-dimensional helical-scan computed tomography using cone-beam projections," Journal of Electronics, Information, and Communication Society, J74-D-II, 1108-1114, (1991).
2. D. X. Yan and R. Leahy, "Cone-beam tomography with circular, elliptical and spiral orbits," Phys. Med. Biol. 37, 493-506, (1992).
3. S. Schaller, T. Flohr and P. Steffen,"New efficient Fourier reconstruction method for approximate image reconstruction in spiral cone-beam, CT at small cone angles," SPIE International Symposium on Medical Imaging, February, 1997.
4. G. Wang, T-H Lin, P. Cheng and D. M. Shinozaki, "a general cone beam algorithm," IEEE Trans. Med. Imag. 12, 486-496, (1993).
A cone-beam reconstruction method using 3D backprojection for cone-beam helical scans is described in copending U.S. patent application Ser. No. 09/038,320, entitled, "Method and Apparatus for Reconstructing Volumetric Images in a Helical Scanning Computed Tomography System with Multiple Rows of Detectors," by C. M. Lai, filed on Mar. 11, 1998, of common assignee. In the approach described therein, at each view angle, the projection profile is interpolated from the collected cone-beam data for a slice normal to the z-axis. Such interpolated projection profiles are then convoluted with a well known kernel as in a 2D image reconstruction for all view angles. The convoluted projection profiles from a number of slices at successive z positions are then backprojected to a 3D matrix to reconstruct the volumetric image of the object. In this 3D backprojection, the convoluted projection values are backprojected to the voxels along the rays for which they were measured, and each voxel is backprojected from one convoluted projection value at each view angle. In this cone-beam reconstruction method, the backprojection is computed accurately, but the convolution operation is an approximation.
If the projection profiles were simply backprojected from all view angles without the convolution operation, the spatial resolution image would be highly reduced as if the image were filtered by a very low-pass filter. The purpose of convolution is to compensate for such a low-pass filtering effect. An exact convolution kernel can be derived for such compensation, and an accurate image can be reconstructed by convoluting the projection profile with this kernel. However, it requires that all rays of the projection profiles lie on the same plane in all view angles. Deviation from this coplanar condition will introduce errors into the convoluted projection data. In the conventional CT scanner with a single row of detectors, all projections are either measured from the same slice or interpolated from two parallel slices to the same slice for convolution. Therefore, accurate images can be reconstructed.
In a cone-beam system, the projection profiles measured from different view angles are not on the same plane because of the cone angle. For a step-and-shoot scan, the projection profiles measured by the central row of detectors do stay on the same plane in all view angles. Thus the central slice can be reconstructed accurately. However, other slices will contain error as the result of deviation from the coplanar condition. In a helical scan, the condition is worse. At each view angle, the projection profile has to be interpolated from the projection values measured by different rows of detectors to a selected slice for convolution. Therefore, even for the central slice, the interpolated projection profiles do not satisfy the coplanar condition for all view angles.